The minimal radius of Galerkin information for the problem of numerical differentiation

The problem of numerical differentiation for periodic functions with finite smoothness is investigated. For multivariate functions, different variants of the truncation method are constructed and their approximation properties are obtained. Based on these results, sharp bounds (in the power scale) of the minimal radius of Galerkin information for the problem under study are found. (c) 2023 Published by Elsevier Inc.

Automated summary

The problem of numerical differentiation for periodic functions with finite smoothness is examined. Various truncation methods are developed for multivariate functions and their approximation properties are determined. Based on these findings, sharp bounds in terms of power scale are derived for the minimum radius of Galerkin information for the studied problem.